Abstract
The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type Delta correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type Delta, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.